Choquet integral with respect to the generalized L-measure and its application

In this paper, a generalized L-measure, denoted L
G
-measure, is proposed. This new measure is proved that it is of closed form with infinitely many solutions, and can be considered as an extension of the three well known measures, additive measure, λ-measure and P-measure, respectively. Furthermore, it is a completed multivalent fuzzy measure, and not only including the smallest fuzzy measure, P-measure, but also attaining to the largest fuzzy measure, B-measure. It has more infinitely many fuzzy measure solutions than L-measure, and L
δ
-measure. By using 5-fold cross-validation MSE, a real data experiment is conducted for comparing the performances of a multiple linear regression model, a ridge regression model, and the Choquet integral regression model with respect to P-measure, λ-measure, L-measure, L
δ
-measure, and L
G
-measure, respectively. The result shows that the Choquet integral regression models with respect to the proposed L
G
-measure outperforms other forecasting models.